Join extruded vertex with edge
Subdivide is a bad option in your situation because you get more verticals than you need.

The fastest way, in my opinion, is to manage this with a loop cut.


Loop Cut CTRL+R and slide to the position where you want to connect your vertex
Select your vertices and merge ALT+M them


 

You could the same with the knife tool (K). However you can't guarantee  for a good mesh flow if you do so. 
With Loop Cuts you are most of the time on the good side.